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asambeis [7]
2 years ago
10

To determine the trajectory of the movement of a material point in the xOz plane that is subjected simultaneously to oscillation

s x (t) = A * sin π(t + 1) and y (t) = A * sin (πt + π / 2).
Physics
1 answer:
nasty-shy [4]2 years ago
4 0

We are to show that the given parametric curve is a circle.

The trajectory of a circle with a radius r will satisfy the following relationship:

(x-x_c)^2 + (y-y_c)^2 = r^2

(with (x_c,y_c) being the center point)

We are given the x and y in a parametric form which can be further rewritten (using properties of sin/cos):

x(t) = A\sin \pi(t+1) = A\sin (\pi t + \pi) = -A\sin \pi t\\y(t) = A\sin (\pi t + \frac{\pi}{2}) = A\cos \pi t

Squaring and adding both gives:

x^2(t) + y^2(t) = A^2(-1)^2\sin^2 \pi t + A^2 \cos^2 \pi t = A^2\\\implies x^2 + y^2 = A^2

The last expression shows that the given parametric curve is a circle with the center (0,0) and radius A.


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A car is driving at 85 km/h and the driver spots a stop sign ahead. What coefficient of friction is needed to stop the car at th
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Answer:

μ = 0.0315

Explanation:

Since the car moves on a horizontal surface, if we sum forces equal to zero on the Y-axis, we can determine the value of the normal force exerted by the ground on the vehicle. This force is equal to the weight of the cart (product of its mass by gravity)

N = m*g (1)

The friction force is equal to the product of the normal force by the coefficient of friction.

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This way replacing 1 in 2, we have:

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Using the theorem of work and energy, which tells us that the sum of the potential and kinetic energies and the work done on a body is equal to the final kinetic energy of the body. We can determine an equation that relates the frictional force to the initial speed of the carriage, so we will determine the coefficient of friction.

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Now replacing:

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5 0
3 years ago
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